1. Field of the Invention
The present invention relates to a method for optimizing the location and number of power/ground pads on a power/ground distribution network with multiple voltage domains. More specifically, the invention relates to a method for decreasing an optimization time and securing the minimum number and location of pads in a power distribution network layout by solving problems generated when a conventional pad optimization method is applied to a power/ground distribution network layout using bump bonding and supplementing shortcomings of the conventional pad optimization method.
2. Background of the Related Art
It is very important to provide power to functional blocks constituting an integrated circuit while decreasing IR drop generated in a power/ground distribution network of the integrated circuit below a reference value. This can be achieved by determining the optimized location and number of power/ground pads that provide power such that the worst IR drop in the power/ground distribution network becomes lower than the reference value. In the following description, a pad selected to be used as a power/ground pad is referred to as ‘optimized pad’, an optimization method for analyzing the power/ground distribution network for global pads to find optimized pads is referred to as ‘global optimization method’ and a pad optimization method provided by the present invention is referred to as ‘local optimization method’.
<Power/ground distribution network layout and IR drop analysis method>
A power/ground distribution network is designed on the assumption that the power/ground distribution network has a single voltage domain and optimization is performed using only static IR drop in an integrated circuit, and thus the power/ground distribution network is modeled as a linear resistor network having an independent current source.
The following modified nodal analysis (MNA) is used for static analysis of the power/ground distribution network structure.
[Equation 1]G·X=I
Here, G represents conductance matrix, X represent the vector of a node voltage, and I denotes an independent current source.
The independent current source I is composed of a Thevenin equivalent current source modified from a voltage source and a load current source that represents power consumption of a functional block.
Once the equation 1 for the power/ground distribution network structure analysis is constructed, the solution (node voltage) of the power/ground distribution network structure can be obtained through a direct method or an iterative method [Reference: T Sato, M. Hashimoto and H. Onodera, “Successive pad assignment algorithm to optimize number and location of power supply pad using incremental matrix inversion”, Asia and South Pacific Design Automation conference, pp. 723-728, 2005].
<Load current source modeling method for analysis of power/ground distribution network>
The load current source, an element of the vector of the current source in the equation 1, represents power consumption of a functional block in the power/ground distribution network and is calculated based on the size and power consumption of the functional block. Accordingly, the worst IR drop is generated at a node to which the load current source belongs, and thus the node having the load current source is used as an IR drop observation node.
In a prior art, the arrangement of load current sources is simplified by equally spacing the load current sources in the functional block or placing them at the center of the functional block.
<Global optimization method>
The global optimization method globally reduces the worst IR drop in the power/ground distribution network according to the following method and finds pads one by one based on greedy search.
FIG. 1 is a flowchart of a conventional global optimization method for optimizing power/ground pads of an integrated circuit.
Referring to FIG. 1, one of given pad candidates is selected and a power/ground distribution network is analyzed in step S1.
An observation node having the worst IR drop is found from observation nodes of the power/ground distribution network, the worst IR drop is calculated, and the pad candidate and worst IR drop value are stored in a temporary memory in step S2.
A pad candidate which is not selected from the given pad candidates is selected and the steps 1 and 2 are repeated in step S3.
After all the pad candidates are used, a pad candidate giving a minimum worst IR drop is determined as a pad and stored in a pad list in step S4.
The optimization process is returned to the step 1 when the worst IR drop calculated with the determined pad does not satisfy constraints and the optimization process is ended when the worst IR drop satisfies the constraints in step S5. Here, the pad candidate determined as a pad among the pad candidates is excluded.
The above-described optimization method analyzes the power/ground distribution network using all the given pad candidates to find a single optimized pad, and thus the optimization time is affected by the number of the given pad candidates. Accordingly, the aforementioned optimization method is not suitable for recent integrated circuit layouts using bump bonding which requires a large number of pads since a long time is taken for the optimization.
<Setting of optimization constraints>
To verify the validity of optimized pads, it is checked whether IR drops of observation nodes and current flowing through pads in the power/ground distribution network satisfy the constraints after optimization to finally determine whether the pads are optimized. That is, a voltage is applied to pads selected as optimized pads and whether the worst IR drop in the power/ground distribution network is lower than a reference value and whether the currents flowing through the pads selected as the optimized pads are smaller than a reference value are checked. When the worst IR drop at the node is lower than the reference value and the current of the pad is smaller than the reference value, it is determined that the optimization is completed.
A technique of providing optimized location and number of power/ground pads that provide power such that the worst IR drop in a power/ground distribution network becomes below an allowable reference value is required. However, when the conventional global optimization method is applied to the recent integrated circuit layouts using bump bonding, the global optimization method, the use of a single voltage domain, and optimization constraints that determine optimization only using a target IR drop and maximum current flowing through pads may increase the optimization time or take an unnecessary time for optimization and bring about inappropriate pad arrangement.